The left-back put pen to paper on a five-year contract at Stamford Bridge, becoming Frank Lampard’s third major signing of the summer in a deal worth around £50 million.
The Blues have already added Timo Werner and Hakim Ziyech to their ranks, but Chilwell represents much-needed defensive cover.
Reacting to the move on his Instagram page, Grealish said: ‘Congratulations brother ❤️❤️❤️.’
Chelsea are also expected to sign centre-back Thiago Silva, who played his last game for Paris Saint-Germain in their 1-0 Champions League final defeat to Bayern Munich.
The defender – who turns 36 next month – is set to undergo a medical on Thursday and will bring lots of experience to a Chelsea backline that is in need of a leader.
Silva has won seven league titles with PSG and earned 89 caps for his country Brazil.
Former Blues midfielder Craig Burley backs both Chilwell and Silva to be good additions for Lampard’s side.
‘He [Chilwell] didn’t have a good second half of the season after injuries, the first half was pretty good,’ Burley told ESPN FC earlier this week.
On Silva, Burley said: ‘The guy can defend. He’s just been part of a team that’s got to the Champions League final and lost to the best team on the planet at the moment in Bayern Munich.
‘It makes sense for me. It’s not ideal signing a [soon to be] 36-year-old, but it’s a fit 36-year-old who’s got good character, good experience and can still play.’